So when the piece in the center needs to expand, it has to push both sides 500mm?
Why would it catch? Why would it split? There is nothing holding it in position other than gravity and a little friction. BTW this is 1800mm and has moved freely for 10 years.
This is nothing more than a basic frame and panel construction, some of the members don't seem to understand that and think I've broken some long held woodworking rule.
In my (exaggerated) example, it's nothing more than a large FLOATING panel that just happens to be made of several pieces glued together. The same process used in a much narrower gate would pose no problems as many seem to think.
I did not break the frame and panel rules. Please don't call the wood police.
Your approach is somewhat unconventional, although your understanding of wood expansion/contraction is good. It's true that total expansion and shrinkage of, say, 10 tangentially sawn red pine boards 100 mm wide at their driest in service will be the same whether joined together into one wider panel of 1000 mm wide or individually. In this example let's say each board expands and contracts by 2 mm over the seasons, i.e., in this case between 100 and 102 mm meaning a total range of movement of 20 mm annually. That is, as you evidently understand, 10 boards X 2 mm of expansion/contraction = 20 mm, or those 10 boards glued together to make a 1000 mm wide panel which would result in 20 mm expansion/contraction.
Just for fun I did some sums using your 1800 mm wide panel made out of tangentially sawn (T&G boards are always tangentially sawn) red pine (
pinus resinosa) native to NE America, [no idea what you actually used] varying between 14 and 20% MC, fairly typical for wood used externally here in the UK. It results in panel size change of approximately 26 mm, or about 2 mm per board for each of the 14 boards in your panel. Assuming expansion/contraction of the panel occurs from its centre point the depth of the groove at either edge would need to be a minimum of 13 mm to avoid the edge of the panel popping out of its groove. Most workers would aim for a greater margin of safety than this, e.g., a groove perhaps 18 - 20 mm deep, or they'd do the conventional thing, and not glue the tongues and grooves together and fit the boards with a bit of wriggle room at each of their edges, plus ideally, fixed at each board's centre point, and into a groove if the boards go into a groove; not all do go into grooves, because some go into rebates, and some are just laid over some framing.
Having said all the above, I don't know what wood species you used in your photographed piece, therefore nor do I know the typical shrinkage/expansion factor I needed to plug into the formula I use for the calculation I can undertake, and I don't know the typical range of MC your piece experiences there in California.
Still, it's interesting that you've got away without a failure with one wide panel as you have for the last ten years. Sometimes the unconventional works. Slainte.